System and method for estimating the probability of movement of access points in a WLAN-based positioning system

ABSTRACT

Methods of and systems for estimating the probability of movement of access points in a WLAN-based positioning system are provided. Disclosed are methods to quantify the probability that a particular location estimate of a mobile device made by a Wi-Fi based positioning system is correct to within an arbitrary accuracy. Implementations use observed access point cluster size, age information for access point location determination, and/or the probability that one or more access points detected by the mobile device have relocated based on historic information about the movement of a collection of access points to make the probability determinations.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation of and claims the benefit under 35U.S.C. §120 of U.S. patent application Ser. No. 12/760,780, filed onApr. 15, 2010, entitled System and Method for Estimating the Probabilityof Movement of Access Points in a WLAN-based Positioning System, whichclaims the benefit under 35 U.S.C. §119(e) of U.S. Provisional PatentApplication No. 61/316,980, filed on Mar. 24, 2010, entitled System AndMethod For Resolving Multiple Location Estimate Conflicts In AWLAN-Positioning System, each of which is herein incorporated byreference in its entirety.

This application is related to the following U.S. patent applications,the contents of which are hereby incorporated by reference:

-   -   U.S. patent application Ser. No. 11/261,988, entitled        Location-Based Services That Choose Location Algorithms Based On        Number Of Detected Access Points Within Range Of User Device,        filed on Oct. 28, 2005, now U.S. Pat. No. 7,305,245;    -   U.S. patent application Ser. No. 11/359,144, entitled Continuous        Data Optimization Of New Access Points In Positioning Systems,        filed on Feb. 22, 2006, now U.S. Pat. No. 7,493,127;    -   U.S. patent application Ser. No. 11/678,301, entitled Methods        And Systems For Estimating A User Position In A WLAN Positioning        System Based On User Assigned Access Point Locations, filed on        Feb. 23, 2007, now U.S. Pat. No. 7,471,954;    -   U.S. patent application Ser. No. 11/625,450, entitled System and        Method For Estimating Positioning Error Within A WLAN-Based        Positioning System, filed on Jan. 22, 2007; and    -   U.S. patent application Ser. No. 12/760,777, entitled System and        Method for Resolving Multiple Location Estimate Conflicts in a        WLAN-Positioning System, filed on Apr. 15, 2010.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The invention generally relates to position estimates in a WLAN-basedpositioning system, and, more specifically, to estimating theprobability that a position estimate is correct.

2. Description of Related Art

The U.S. patents and applications incorporated above and assigned toSkyhook Wireless, Inc. describe a Wi-Fi Positioning System (WPS) thatuses the natural properties and widespread deployment of 802.11 accesspoints (APs herein) to deliver precise positioning data to any Wi-Fienabled device.

In such a WPS, APs provide a valuable method for determining thelocation of mobile wireless devices. Accurate knowledge of AP locationsis essential to mobile location determination, and the relocation of APsposes a significant challenge to mobile location systems. For example,when a mobile device observes APs that have been relocated, itsobservations can conflict with stored AP location information and leadto location errors.

BRIEF SUMMARY OF THE INVENTION

Under one aspect of the invention, a method of and system for measuringand recovering from mobile location errors due to access pointrelocation is provided.

Under another aspect of the invention, a method of estimating thelikelihood of a Wi-Fi enabled device being located within an estimatedgeographical area includes the Wi-Fi enabled device receiving signalstransmitted by Wi-Fi access points in range of the Wi-Fi enabled device.The method also includes consulting a reference database to determinefor each of at least one of the Wi-Fi access points from which signalswere received a last-known estimated position of the Wi-Fi access pointand time information associated with the last-known position fordescribing the age of the last-known position relative to otherinformation in the reference database. The method further includesestimating, based on the last-known position, associated timeinformation, and number of Wi-Fi access points from which signals werereceived the likelihood of the Wi-Fi enabled device being located withinan estimated geographical area and displaying on a display deviceinformation based on the estimated likelihood of the Wi-Fi enableddevice being located within the estimated geographical area.

Under another aspect of the invention, estimating the likelihood of theWi-Fi enabled device being located within the estimated geographicalarea is further based on information that characterizes the probabilitythat a Wi-Fi access points has moved from its corresponding last-knownposition. The probability is based on the relative age of saidlast-known position.

Under a further aspect of the invention, the method also includesestimating, based on the last-known position and associated timeinformation, a plurality of likelihoods of the Wi-Fi enabled devicebeing located within a corresponding plurality of estimated geographicalareas and displaying on a display device information based on theplurality of estimated likelihoods of the Wi-Fi enabled device beinglocated within the corresponding plurality of estimated geographicalareas.

Under an aspect of the invention, the method also includes consulting anhistorical dataset to determine for at least one of the Wi-Fi accesspoints from which signals were received information describing pastrelocations for said at least one Wi-Fi access point. The estimating thelikelihood of the Wi-Fi enabled device being located within theestimated geographical area is further based on the informationdescribing past relocations for the at least one Wi-Fi access point.Optionally, the information describing past relocations for the at leastone Wi-Fi access point includes an average movement frequency for the atleast one Wi-Fi access point. Optionally, the information describingpast relocations for the at least one Wi-Fi access point includes anaggregate average movement frequency based on a collection of movementdata for a plurality of Wi-Fi access points.

Under yet another aspect of the invention, a method of estimating thelikelihood of a Wi-Fi enabled device being located within an estimatedgeographical area includes the Wi-Fi enabled device receiving signalstransmitted by Wi-Fi access points in range of the Wi-Fi enabled device.The method also includes consulting a reference database to determinefor each of a plurality of the Wi-Fi access points for which signalswere received a last-known estimated position of the Wi-Fi access pointand determining that at least a first set of the Wi-Fi access points forwhich signals were received have moved from their correspondinglast-known estimated positions based on the last-known estimatedpositions for at least a second set of Wi-Fi access points for whichsignals were received. The method further includes estimating, based onthe number of Wi-Fi access points of the first set and the number ofWi-Fi access points of the second set, the likelihood of the Wi-Fienabled device being located within an estimated geographical area anddisplaying on a display device information based on the estimatedlikelihood of the Wi-Fi enabled device being located within theestimated geographical area.

Under a further aspect of the invention, the method also includesestimating, based on the number of Wi-Fi access points of the first setand the number of Wi-Fi access points of the second set, a plurality oflikelihoods of the Wi-Fi enabled device being located within acorresponding plurality of estimated geographical areas and displayingon a display device information based on the plurality of estimatedlikelihoods of the Wi-Fi enabled device being located within thecorresponding plurality of estimated geographical areas.

Under still another aspect of the invention, estimating the likelihoodof the Wi-Fi enabled device being located within the estimatedgeographical area is further based on information that characterizes theprobability that at least one of the Wi-Fi access points of the firstset has moved from its corresponding last-known position, theprobability being based on the number of Wi-Fi access points of thefirst set and the number of Wi-Fi access points of the second set.

Under another aspect of the invention, the method also includesconsulting the reference database to determine for at least a firstWi-Fi access points from which signals were received a last-knownestimated position of the first Wi-Fi access point and time informationassociated with the last-known position for describing the age of thelast-known position relative to other information in the referencedatabase. The estimating the likelihood of the Wi-Fi enabled devicebeing located within an estimated geographical area being further basedon the last-known position and associated time information of the firstWi-Fi access point.

Under a further aspect of the invention, a method of estimating thelikelihood of a Wi-Fi enabled device being located within an estimatedgeographical area includes the Wi-Fi enabled device receiving signalstransmitted by at least one Wi-Fi access point in range of the Wi-Fienabled device. The method also includes extracting information from thesignals received that identifies each of the at least one Wi-Fi accesspoints from which signals were received and consulting a referencedatabase to determine for at least one of the Wi-Fi access points fromwhich signals were received a set of information identifying acorresponding set of Wi-Fi access points from which signals are expectedto be received when the Wi-Fi enabled device receives signals from theat least one Wi-Fi access point of the plurality. The method furtherincludes estimating the likelihood of the Wi-Fi enabled device beinglocated within an estimated geographical area based on a comparison ofthe information identifying Wi-Fi access points from which signals werereceived and the set of information identifying the corresponding set ofWi-Fi access points from which signals are expected to be received anddisplaying on a display device information based on the estimatedlikelihood of the Wi-Fi enabled device being located within theestimated geographical area.

Under yet another aspect of the invention, a method of estimating thelikelihood of a Wi-Fi enabled device being located within an estimatedgeographical area includes the Wi-Fi enabled device receiving signalstransmitted by Wi-Fi access points in range of the Wi-Fi enabled deviceand extracting information from the signals received that identify eachof a plurality of the Wi-Fi access points from which signals werereceived. The method also includes consulting a reference database todetermine if the identity of each of the plurality of the identifiedWi-Fi access points from which signals were received are present in thereference database. The method further includes estimating thelikelihood of the Wi-Fi enabled device being located within an estimatedgeographical area based on the number of Wi-Fi access points from whichsignals were received and for which identities are present in thereference database, and displaying on a display device information basedon the estimated likelihood of the Wi-Fi enabled device being locatedwithin the estimated geographical area.

BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWINGS

FIGS. 1A-B illustrate a method for calculating location estimates andcenter probabilities for a mobile device using a Wi-Fi PositioningSystem.

FIG. 2 shows a scenario in which a mobile device simultaneously observesAPs from two discrete clusters.

FIG. 3 shows an example in which a mobile device detects two clusters ofequal size.

FIG. 4 shows an example in which an access point scanning device detectstwo clusters, one cluster having moved after the last locationconfirmation scan.

FIG. 5 shows an example in which an access point scanning device detectstwo clusters, one cluster having moved after the last locationconfirmation scan.

FIG. 6 shows an example in which a mobile device detects two clustershaving differing numbers of access points.

FIG. 7 shows an example in which a mobile device detects a singlecluster.

DETAILED DESCRIPTION

Preferred embodiments of the invention provide methods of and systemsfor measuring and recovering from mobile location errors due to Wi-Fiaccess point relocation. The embodiments described herein quantify theprobability that a particular location estimate of a mobile device madeby a WPS is correct to within an arbitrary accuracy. Implementations ofthe invention estimate the probability that one or more APs detected bythe mobile device have relocated. In one illustrative example, theprobability is estimated based on all or a subset of data present in theWPS that describes, in aggregate, the movement of many APs in thesystem. In another example, a system estimates such a probability upondetermining that at least one of the APs observed by a mobile device hasmoved, such as, when location information associated with the observedAPs is in conflict.

Certain embodiments of the invention build on techniques, systems andmethods disclosed in the U.S. patents and applications incorporatedabove. The present techniques, however, are not limited to systems andmethods disclosed in the incorporated patents and applications. Thus,while reference to such systems and applications may be helpful, it isnot believed necessary to understand the present embodiments orinventions. For example, those applications taught specific ways togather high quality location data for APs (also called “scan data”) sothat such data may be used to estimate the geographic location of aWi-Fi-enabled device utilizing such services and techniques. Bycollecting location data repeatedly from the same location and recordingthe date of each scan event in a database, it is possible to observe theappearance and disappearance of APs over time. In some cases, appearingAPs will be new devices that have not appeared in the databasepreviously. Similarly, disappearing APs may be removed from service andnever again appear in the database. Techniques to mitigate the negativeeffects of APs appearing and disappearing over time are addressed inother patent applications assigned to the assignee of the presentapplication and are not discussed in detail herein. However, there is athird case in which an AP disappears from one location and appears inanother location. The use of repeated scanning and maintenance of atime-indexed database of scan data facilitates the observation of APmovement.

The ability to track AP movement allows a reference database containingAP location information to be corrected to address obsolete AP locationinformation, and tracking also produces valuable statistics that can beused to infer the movement of APs, even if they have not been scanned intheir current locations. Mining the database yields empiricalprobability distributions on the frequency with which APs relocate andthe associations between groups of APs that move together. Theseprobability distributions are discussed in greater detail below.

Mobile location error is typically quantified using horizontalpositioning error (HPE). Given a location estimate and an arbitraryprobability threshold, HPE expresses the radius of a circle centered onthe location estimate that is large enough to include the mobile'sactual location with the desired probability. For instance, if alocation technology is extremely accurate, it could be said that thereis a 95% probability that the mobile's actual location is within 10meters of a location estimate. For a less accurate system, the HPE mightbe 1000 meters for a 95% probability threshold.

Detecting and recovering from location errors caused by AP movementrequires a means of quantifying the probability that stored AP locationinformation is correct. To that end, implementations of the inventionemploy records of the age of information in the database and theassociations between different APs. That is, relationships between APsthat have been observed simultaneously to form groups, called clustersherein, are used to quantify the probability values. Further, a family,which is a cluster that relocates as a single group, can be used in thesame way. In general, one would expect a family to be made up of APsthat are owned by a single entity.

FIG. 2 depicts a scenario in which a mobile device simultaneouslyobserves APs from two discrete clusters. The database lists the 3 APs inthe first cluster as residing in Boston, and 2 APs in the second clusteras residing in from Chicago. Since the transmission ranges of the APs isfar smaller than the distance from Boston to Chicago, the database mustcontain incorrect information about at least one of the two clusters. Inother words, both clusters are currently located in either Boston orChicago, but the mobile cannot be absolutely certain which assumption iscorrect. As a result, the positioning algorithm assigns centerprobabilities to two separate location estimates, one in Boston and onein Chicago.

Even when the mobile observes only a single cluster of APs, there issome finite probability that the observed cluster is a family that hasbeen relocated since the last time their location was confirmed. Thus,the center probability, P, applies to scenarios with any number ofobserved AP clusters.

In one implementation of the invention, a method is provided forcalculating the center probability, P, using empirical data on the sizesof families of moved APs and the frequency with which families arerelocated.

FIGS. 1A-B show a method for calculating location estimates and centerprobabilities in a variety of scenarios. First, the mobile devicedetects surrounding APs (step 71) and counts the total number ofobserved APs. Next, it consults the database to determine the number ofseparate clusters and the number of APs in each cluster (step 72). Inother words, because the reference database has the coordinates of allscanned APs, it is able to separate the APs (or group of APs) that arefar away from each other (when the distance between APs is larger thansome large enough threshold). Each cluster is associated with the lasttime that it was observed by the scanner (i.e., the last time locationinformation on the cluster was updated in the database containing theinformation about the location coordinates of all APs and last time anAP was observed by the scanner) (step 73). The term “scanner” as usedherein describes a device that can detect Wi-Fi APs and also has atrusted and independent source of location information. For example, ascanner device may have both a Wi-Fi radio and a GPS system. Based onthe number of clusters, the number of APs in each cluster, and the ageof the information for each cluster, the invention determines centerprobability, P, values and other metrics as described in greater detailbelow.

For example, if only a single cluster is detected (at step 74), then themethod determines the probability that the single cluster has movedsometime after the last confirmation of the location of the APs of thecluster has been performed. This is also called a “no location”probability herein. Meanwhile, if more than one cluster is detected,then a conditional probability of relocation for each of the APs isdetermined (step 76). That is, upon the condition of a conflict inlocation arising from the observation of APs (or clusters) that shouldnot be detected simultaneously based on their last-known location, aprobability that one of the APs (or clusters) has relocated isdetermined. In addition, the relative size of the clusters is comparedwith an empirical data set to determine the relative likelihood thateach cluster of APs has moved sometime after the last confirmation ofthe location of the APs of the clusters has been performed (step 76).These techniques are set forth in more detail below.

Next, the method calls for determining the center probabilities for eachdetected cluster. As set forth in greater detail below, differentformulas are used to determine these values depending on the number ofclusters detected.

The method set forth above and shown in FIGS. 1A-B is described ashaving certain steps performed on a mobile device. While the initialsearch for APs within range of the mobile device is performed by themobile device, any of the other steps can be performed on the mobiledevice or a remote computer system.

Probability of AP Movement

Given up-to-date knowledge of AP locations, the actual location of themobile device is accurately modeled with a radially-symmetricprobability distribution centered at the estimated mobile location(location center). However, when the validity of AP location informationis uncertain due to AP relocation, the location estimation error can bequantified with two parameters. The first parameter is the radius aboutthe location center within which the mobile resides with a givenprobability, conditioned on the fact that the location center isaccurate to an arbitrary precision. The second parameter is the locationcenter probability, P, which is accurate to an arbitrary precision.

Given a database of AP locations measured over time, we construct anapproximation to the empirical cumulative distribution function (CDF) todescribe the conditional probability that a single AP will haverelocated within a specified time interval given that the AP has beenmoved (e.g., a conflict exists between locations of observed APs). Knownmethods may be used to approximate the CDF from the empirical dataset ofAP that have moved. Because the database necessarily spans only a finitetime interval, the CDF must saturate to probability 1 at the age of theoldest data. Thus, as more data is collected and the time spanned by thedatabase increases, the CDF will be updated to reflect improvedknowledge of the long-term relocation behavior of APs.

In one implementation of the invention, the CDF that a given AP willhave relocated as a function of the time since it was last observed bythe scanner is approximated. Time, t, is measured in units of months,and the approximation of the CDF is defined as Y(t), whereY(t)=a, if 0<t≦h ₀,Y(t)=bt+c, if h ₀ <t≦h ₁,Y(t)=1, if h ₁ <t.  (1a)and a, b, c, h₀, h₁ are some constants, which are found empirically byanalyzing the database of moved APs. One example of Y(t) is given by theformulaY(t)=0.02, if 0<t≦3,Y(t)=(2.51t−5.54)/100, if 3<t≦42,Y(t)=1, if 42<t,  (1)which corresponds to step 76 of FIG. 1B.

The values of Y(t) represent a probability weight that the AP has beenmoved during the last t months, given that the last time it was scannedwas t months ago, and given that the system has determined the AP is ina set of observed APs, one or more of which have moved.

Function (1) was determined by analyzing the database of moved APs. Thisdatabase has all the information about moved APs, including the historyof all locations of all detected moved APs and time of each AP beingobserved at each location.

As the database ages and contains a growing time series of scanned data,Y(t) is updated as follows:

$\begin{matrix}{{{{Y(t)} = \frac{84}{100\left( {42 + n} \right)}},{if}}{{0 < t \leq 3},{{Y(t)} = {{\frac{41.16 + n}{\left( {39 + n} \right)\left( {42 + n} \right)}t} - \frac{2.16}{39 + n}}},{if}}{{3 < t \leq {42 + n}},{{Y(t)} = 1},{if}}{{42 + n} < {t.}}} & (2)\end{matrix}$

-   -   where n=1, 2, 3, . . . represents the number of 6 month        intervals since the first use of the function.

The conventional definition of HPE works well when the distribution oferror in a location estimate is unimodal. Errors arising from noisyrange estimation can be considered unimodal, but errors due to APrelocation are multimodal and not well quantified by HPE. For example,in a scenario in which a mobile observes two APs, one AP has correctlocation information in the database, but the other AP has beenrelocated from 100 kilometers away. The database has not been updated toreflect the relocation of the second AP, so it supplies the mobile withincorrect location information. If a single location estimate isconstructed and a single circle drawn around it to express HPE, theradius will be on the order of 50 kilometers. However, if the underlyingstructure of the scenario is examined, it is seen that the locationerror is bimodal, and is better described with two circles,corresponding to each of the two APs. Each circle has its own HPE andcenter probability, P, which expresses the relative confidence in theinformation about each of the two APs in the database.

Clusters Of Equal Size

FIG. 3 shows an example in which the mobile device 21 detects two equalsize clusters of APs: one cluster of 3 APs from New York 22 and onecluster of 3 APs from Miami 23. Note that a cluster might be as small asa single AP and has no upper limit on the number of members.

When a mobile device observes multiple APs whose locations as recordedin the database should preclude them from being observed simultaneously,the mobile device recognizes that one or more APs must have relocated.More generally, the mobile device may observe multiple clusters of APs,and one or more clusters may have relocated as a family unit. Becauselocation estimation using any of the individual clusters would lead todisparate center locations, the mobile device must resolve theconflicting information in order to decide on a single location center.

Under one implementation, the conflicting location information isresolved by using the age of the newest information on each cluster.Function Y(t) shows that the probability of obsolescence of measurementinformation increases with the age of the measurement, so newermeasurements are considered to be more reliable. Thus, the mosteffective method of choosing a location center is to assume that thecluster with the most recent measurement data has not relocated. Basedon the difference in ages between the measurements of each cluster, themobile device can then express its confidence in the chosen locationcenter.

For example, consider the case where the mobile has observed twoclusters of n APs. Each AP in each cluster is assigned an arbitraryindex from 1 to n. The time since AP, of cluster 1 was last observed isdenoted t_(i), and the time since AP_(j) of cluster 2 was last observedis T_(j). The ratio, r, can be calculated as follows:min(t _(i))=the smallest number among t ₁ ,t ₂ , . . . ,t _(n);min(T _(j))=the smallest number among T ₁ ,T ₂ , . . . ,T _(n).

$r = \frac{Y\left( {\min\left( t_{i} \right)} \right)}{Y\left( {\min\left( T_{j} \right)} \right)}$

The parameter P₁ is assigned to the location estimate based on cluster 1and probability parameter P₂ is assigned to the location estimate basedon cluster 2. P₁ and P₂ are calculated according to the followingequations (this corresponds to step 78 of FIG. 1B):

$\begin{matrix}{{P_{1} = \frac{1}{1 + r}},{P_{2} = \frac{r}{1 + r}}} & (3)\end{matrix}$

In practice, there are several ways to apply P₁ and P₂. For example,only the location corresponding to the maximum center probability couldbe reported. Alternatively, a probability threshold could be set and alocation only reported if one of the two center probabilities exceedsthat threshold. If neither center probability exceeds the threshold(note that they are complementary and cannot both exceed 0.5simultaneously), then the location estimate could be considered to betoo unreliable, and a “no location” result reported. As a thirdpossibility, both location estimates along with their associated centerprobabilities could be reported.

Cluster Movement

The sizes of observed clusters also affect the probability that theclusters have relocated. It has been discovered that small families aremuch more common than large families because there are a relativelysmall number of organizations that relocate with large numbers of APs.Thus, a large cluster is unlikely to be made up of a single family, andlarger clusters are less likely to have been relocated.

Under another implementation of the invention, statistics based on theratio of cluster sizes, a method for updating cluster information in thedatabase, and a method for identifying and tracking families of APs asthey relocate is described. As stated above, it is assumed that thescanning equipment used to compile the database possesses accuratelocation information independent of observed APs, so the database hashigh precision information regarding where and when each AP wasobserved. For example, the scanning equipment used to compile thedatabase may use a GPS system to determine its position when detectingAPs in a given geographical area.

For each scan in the database, any APs that have been observedsimultaneously as belonging to the same cluster are identified during ascanning event to update and/or create the reference database. Then,whether any of the APs in the cluster have been relocated since the lasttime they were observed is also identified. If one or more APs have beenrelocated, previous observations are consulted to see if any of therelocated APs were moved as a family from their previous location(s).Taking the general definition that a family can be as small as one AP,each instance of family relocation is examined as follows. Each time afamily relocates, the number of APs in the family and the number of APsnot in the family is counted that combined to form the new cluster. Thatis, the number of relocated APs is compared to the number of APs thatwere not relocated. The notation

i→j

is used to represent the situation in which a family of i relocated APsis observed at the same time as j APs that have not been relocated sincethe last scan. In other words, the scanning device detected i new APsand j old APs at the same time and place.

FIG. 4 shows an example in which a scanner located in Boston 31 observes1 AP that has been moved from Dallas 32 and 2 APs that have remained,unmoved, in Boston 33 since the last time they were scanned. In thiscase, one pair 1→2 would be recorded.

Referring to FIG. 5, if the same APs had been observed by a scanner inDallas 41, then the scanner would conclude that the two APs from Boston43 had been moved, and 1 AP from Dallas 42 remained, unmoved, and record2→1.

After recording the total number of different pairs i→j, parameterK_(ij) is defined to describe the empirical probability that, givensimultaneously observed clusters of size i and j with conflictinglocation information, the cluster of size i was relocated (for the casewhen i≠j) (this corresponds to step 76 of FIG. 1B). Thus,

$\begin{matrix}{{K_{ij} = \frac{\left. {{number\_ of}{\_ pairs}{\_ i}}\rightarrow j \right.}{\left. {{total\_ number}{\_ of}{\_ pairs}{\_ i}}\rightarrow\left. {{j\_ and}{\_ j}}\rightarrow i \right. \right.}}{{{and}\mspace{14mu}{vice}\mspace{14mu}{versa}},}} & (4) \\{K_{ji} = {\frac{\left. {{number\_ of}{\_ pairs}{\_ j}}\rightarrow i \right.}{\left. {{total\_ number}{\_ of}{\_ pairs}{\_ i}}\rightarrow\left. {{j\_ and}{\_ j}}\rightarrow i \right. \right.}.}} & (5)\end{matrix}$

When i=j, K_(ij)=½. Therefore, K_(ij)+K_(ji)=1.

In order to keep the values of K_(ij) as accurate as possible, it ispreferred to recalculate them periodically to reflect new scan data.

Clusters of Equal Age

In another implementation, a method is described for assigning centerprobabilities to location estimates based on two clusters when one ofthe clusters has been relocated and database information on bothclusters is of the same age. In this case, the cluster sizes are used todetermine the probability that either of the two clusters was relocatedas a family.

FIG. 6 shows a scenario in which a first cluster 52 and a second cluster53 are observed simultaneously by the mobile device 51, but the locationinformation in the database indicates that the clusters are separated bya distance much greater than the transmission range of the APs. Thefirst cluster consists of n APs and the second cluster consists of mAPs. The positioning algorithm assigns center probabilities, P₁ and P₂,based on the most recent observation of each cluster.

It this illustrative example, it is assumed that the databaseinformation is of equal age for both clusters. Therefore, time does notplay any role in the computation of the probabilities of the centerlocation. The following definition for r is used:

$r = {\frac{K_{nm}}{\left( {1 - K_{nm}} \right)}.}$

Center probability P₁ is associated with the location of the firstcluster and center probability P₂ is associated with the location of thesecond cluster. The following formulas define P₁ and P₂ (thiscorresponds to step 78 of FIG. 1B):

$\begin{matrix}{{P_{1} = \frac{1}{1 + r}},{P_{2} = \frac{r}{1 + r}}} & (6)\end{matrix}$

Clusters of Differing Sizes and Ages

In another embodiment of the invention, both cluster size and clusterage (the age of the most recent update on the cluster's location in thedatabase) are used to assign center probabilities (this corresponds tostep 78 of FIG. 1B).

Referring again to FIG. 6, the first cluster 52 is of size n, and thesecond cluster 53 is of size m. The time since AP j of the first cluster52 was last observed is denoted t_(j), and the time since AP k of thesecond cluster 53 was last observed is T_(k). The values of min(t_(i))and min(T_(j)) are determined as set forth above.

Next, the ratio, r, is determined using parameters based on both clustersize ratio, K_(nm), and cluster age, Y, as follows:

$r = \frac{K_{nm}{Y\left( {\min\left( t_{i} \right)} \right)}}{\left( {1 - K_{nm}} \right){Y\left( {\min\left( T_{j} \right)} \right)}}$

Once again, the center probabilities are as follows:

$\begin{matrix}\begin{matrix}{{P_{1} = \frac{1}{1 + r}},} & {P_{2} = \frac{r}{1 + r}}\end{matrix} & (7)\end{matrix}$

Movement of a Single Cluster

Under another implementation, a center probability is determined whenthe mobile device observes only a single cluster. In other words, if themobile device finds only a single cluster of APs, there is someprobability that the cluster has been relocated as a single family, andthat possibility is quantified with a center probability.

FIG. 7 shows a situation in which the mobile device 61 has observed asingle cluster 62 of n APs, and the last time the first AP in thiscluster was updated was t₁ months ago. The second AP in this cluster wasupdated t₂ months ago, and the n^(th) AP was updated t_(n) months ago.As above,min(t _(i))=the smallest number among t ₁ ,t ₂ , . . . ,t _(n).

When a mobile device observes only a single cluster (i.e., there is nocluster conflict), the center probability is calculated as a function offollowing items: (1) the number of APs detected by the mobile devicewhich are known in the database, (2) the number of APs detected by themobile device which are not known and are not in the database, (3) otherAPs expected to neighbor a particular AP and the number of expectedneighbors based on the collection of the history of observation ofscanned results including that AP, (4) the minimum time elapsed from thelast time that location of known APs is confirmed by a scanner,min(t_(i)), and (5) the confidence in the known location of individualAPs that are in the database via a scanner detection. We can find,empirically, from the dataset of moved APs the probability of movementof an AP as a function of these parameters.

The above parameters are now discussed in more detail. A set of APsdetected by a mobile device can be divided into two groups. The firstgroup consists of APs that are present in the database by virtue of ascanner or derived from the locations of other known APs, whoselocations are known with some degree of certainty. For example, when anunknown AP is scanned by the mobile device along with other known APs,then the position of the unknown AP can be estimated using atriangulation based on all known APs that are observed by the mobiledevice. The second group consists of APs that are new and have neitherbeen located by a scanner nor derived from other known APs. Thus, someof the APs present in the database may be associated with a locationthat has been derived from other known APs. Therefore, centerprobability can be calculated as a function of number of known APshaving locations.

Center probability can also be a function of the second group, whichcontains new APs that have been detected along-side of known APs thatwere not found by the scanner at the time of scanning. For example,assume a mobile device observes 2 known APs and 10 unknown APs, and themin(t_(i)) parameter of the cluster of the 2 known APs is equal to 1year. Then, empirically, the probability that the cluster of 2 known APshas been relocated, as a family of APs, can be found from the data setof moved APs, given that the mobile device observed 2 known APs and 10unknown APs, and the min(t_(i)) parameter of the cluster of the 2 knownAPs is equal to 1 year. Therefore, we can also find the empiricalprobability that cluster of 2 known APs has not moved.

Center probability can also be a function of expected neighbors ofcollective set of scanned APs. Based on the past history of observing agiven AP with another set of APs at the time of systematic scanningand/or by detection of other mobile devices a set of expected neighborsis established for any known AP along with an expected number ofneighbors. These measures are based on past observations and the densityof APs in the neighborhood of the given AP. When a mobile device detectsa set of APs, the probability that the observed cluster of APs has beenmoved can be determined based on consistency between the expectedneighbors and what the mobile device observes. Probability that an APhas been moved, given a set of expected neighbors, expected number ofneighbors, APs currently detected by the mobile, and number presentlydetected is determined empirically based on historical data gathered by,for example, scanners.

Center location can also be a function of time. In other words, theprobability that an AP has been relocated can be determined as afunction of time. For example, if an AP has been confirmed at a givenlocation, the probability that the AP is still located in the samelocation after one day is higher than after one year.

Also, the certainty of an estimated location for a particular AP can bedifferent. In other words, upon conducting a scanner survey of an area,the estimated location of an AP may be determined with a high confidence(e.g., 100%) or low confidence. Each AP that is found during a scannerpass is associated with a corresponding confidence. Center locationprobability can be a function of confidence in location of known APs. Inone implementation, the confidence of all known APs detected by a mobiledevice can be estimated by taking the maximum confidence of all thedetected APs.

The probability P_(recent) _(_) _(location) that a given cluster of nAPs did not change its location can be estimated based on a collectionof information on moved APs and moved families of APs (e.g., a “movedAPs” database can contain information including previous and currentlocation coordinates, the date a move was detected by a scanner, thesize of families of APs which have been moved, etc.). Probabilityparameter P_(recent) _(_) _(location) depends on the cluster size n andtime min(t_(i)). In other words, one can find from the moved APsdatabase the following probability depending on two parameters:P _(recent) _(_) _(location) =P _(recent) _(_) _(location)(n,min(t_(i))).  (8)

Probability parameter P_(no location) represents the probability that agiven cluster of n APs has been moved to some other location, which hasyet to be detected yet by a scanner. Thus, the “no location” subscriptas used in this context represents the fact that an affirmative locationcannot be provided until the cluster is detected by a scanner at somelater time. Obviously,P _(no location)=1−P _(recent location)  (9)

The potential measures of probabilities of center location as a functionof the set of parameters given above (e.g., number of scanned APs thatare known in the database, number of scanned APs that are not known andare not in the database, expected neighbors and expected number ofneighbors based on scanned AP data, minimum time elapsed after the lasttime that the location of known scanned APs is confirmed, and confidencein the location of individual known scanned APs) can be foundempirically from the moved APs information.

More than Two Clusters

In another implementation of the disclosed embodiment, the method fordetermining center probabilities is generalized to scenarios in whichthe mobile device detects X clusters of APs, where X can be greater than2. The variable w_(n) is the size of the n^(th) cluster (n=1, 2, 3, . .. X), and T_(n) is the age (measured in months) of the most recent scanof cluster n in the database. Ratio r is determined as follows:

${r_{ij} = \frac{k_{w_{i},w_{j}}{Y\left( T_{i} \right)}}{\left( {1 - k_{w_{i},w_{j}}} \right){Y\left( T_{j} \right)}}},\left( {i,{j = 1},2,3,\ldots\mspace{14mu},{X;{i \neq j}}} \right)$where k_(w) _(i) _(,w) _(j) are K-values, Y is the function given by theformula (1). Next, Q_(n) is defined as follows:

$Q_{n} = {{\frac{1}{1 + r_{n,1}} \cdot \frac{1}{1 + r_{n,2}}}\mspace{14mu}\ldots\mspace{14mu}{\frac{1}{1 + r_{n,{n - 1}}} \cdot \frac{1}{1 + r_{n,{n + 1}}}}\mspace{14mu}\ldots\mspace{14mu}\frac{1}{1 + r_{n,X}}}$

The following probabilities are associated with the location of n^(th)cluster (this corresponds to step 79 of FIG. 1B):

$\begin{matrix}{P_{n} = \frac{Q_{n}}{\sum\limits_{i = 1}^{X}Q_{i}}} & (10)\end{matrix}$

Influence of Environment and History of Particular AP Movement onProbabilities of Center Location.

Above, techniques for defining and estimating the probabilities ofcenter locations of a mobile device were provided. These probabilitieswere based on an analysis of aggregate data, that is, a relatively largecollection of location and movement data for relatively large number ofAPs. However, improvements to those estimates can be made using the APsenvironment and history of a given set of APs. For example, if it isknown from the history of APs (which can be extracted from the moved APsdatabase), that a particular AP relocates once per 6 months on average,and a second AP relocates once per 2 years on average, then thisinformation is taken into account to improve the probabilities estimate.In other words, the variable “freq” representing the average movementfrequency of a particular AP or cluster of APs may be taken intoaccount. In such a case, instead of empirically estimated CDFapproximation function Y(t) (formulas 1 and 2), an empirical estimate ofthe CDF approximation function Y(t, freq) is provided, where the jointprobability distribution of random variables t and “freq” is considered,given that a particular AP (or cluster of APs) is determined to bewithin a set of detected APs, one or more of which have moved.

Another parameter that may affect the accuracy of the center probabilityestimate is the APs environment, or surrounding APs. For example, assumea first AP was detected in the recent past by mobile devices inconjunction with 10 other surrounding known APs on average. A mobiledevice now reports the observation of the first AP along with thedetection of a second known AP, the location of which should precludethe two APs from being observed simultaneously. Assume also that thesecond known AP was previously scanned or observed without any othersurrounding APs. Thus, at least one of the two APs has moved from itspreviously recorded location. This circumstance makes it is very likelythat the first AP has been moved because, in addition to the conflictinglocation situation, the surrounding AP density changed substantially.

Considering another example, a third AP has been reported in the recentpast by mobile devices with 5 known surrounding APs on average, and nowa particular mobile device reports the third AP with 4 unknownsurrounding APs. In this case, it is very likely that the third AP hasbeen moved, because although the surrounding APs density has not changedsubstantially (4 versus 5), and no location conflict exists, the 4presently detected APs are not the same, or a subset of the same, APsthat are expected to be surrounding the third AP. The same would holdtrue were a location conflict to exist.

As one example of the use of an AP's environment parameter in adjustingits corresponding movement probability, a parameter, E, is provided thatdescribes a change in APs surrounding density environment:

${E = \frac{E_{1} + 1}{E_{2} + 1}},$where E₁=“recent average number of known APs detected along with given agiven AP (or a given cluster of APs) by mobile devices” and E₂=“currentnumber of known APs detected along with a given AP (or a given clusterof APs) by mobile devices”. Furthermore, a “density environment”function DE is as follows:DE=max(E,E ⁻¹).When DE>C₁, where C₁ is a threshold constant determined empirically(e.g., C₁=4), then the given AP (or given cluster of APs) is designed ashaving moved from its previous known location.

In general, all 3 parameters t, “freq” and DE can be combined in theestimation of center probability. Thus, instead of empirically estimatedCDF approximation function Y(t) (formulas 1 and 2), an empiricallyestimated CDF approximation function Y(t, freq, DE) is provided wherethe joint probability distribution of random variables t, “freq” and DEare considered, given that an AP (or cluster of APs) is determined to bewithin a set of detected APs, one or more of which have moved.

In the case of single cluster observed by the mobile device, theempirically estimated parameter P_(recent) _(_) _(location) is providedas a function of cluster size n, time min(t_(i)), “freq”, and DE asfollows:P _(recent) _(_) _(location) =P _(recent) _(_) _(location)(n,min(t_(i)),“freq”,DE),andP _(no location)=1-P _(recent location).

Known-in-Advance Location Bias Correction

Above, the meaning and techniques for determining K_(ij) parameters, orK-values were described. Those techniques relied on knowing the groundtruth location during scanning. In other words, while scanning andrecording all possible pairs i→j, a highly accurate geographicallocation was known. Typically, an accurate geographical location is onlyknown when using GPS or some other reliable positioning technology.

However, there are some locations (e.g., indoors locations) when GPS orany other, typically accurate, positioning technology does not work oris not reliable. This means that it is possible that the locationinformation for some APs in the reference database may be biased tocertain known-in-advance locations, where a “known-in-advance” locationis one that is known with a relatively high degree of accuracy. Incertain implementations, it is desirable to ensure this bias does notaffect the accuracy of the K-values for the entire distribution of allgeographical locations of all possible AP observations. Note that theentire distribution consists of a first portion of data for which thegeographical location was known with high precision during datacollection and a second portion of the data for which the geographicallocation was not known or was inaccurate (e.g., locations where GPS doesnot work).

In such a case, a sufficiently large (e.g., on the order of 10,000samples) number of AP observation samples containing the informationabout i→j pairs from the geographical locations where GPS location didnot work can be selected. For each of the selected observations, anaccurate geographical location can be determined using other means, andthat location replaces the missing or inaccurate location information inthe reference database. At this point, the updated data can then bereprocessed, as set forth in detail above. This will help to increasethe diversity of the samples and reduce any potentially existing bias inthe K-value estimations.

There may be instances in which there exist an insufficient number ofsamples having manually corrected location data to reduce potentiallybiased K-values as described above. However, it may still be desirableto reduce such bias. In such a case, unbiased K-values can be estimatedfrom the known-in-advance scan locations statistics as set forth below.

The variable N is the total number of existing different families of APsin the known-in-advance possible scan population, and M is the totalnumber of APs in the known-in-advance possible scan population.Proportion (weight) w₁ represents the proportion of all 1-size familiesof APs among N families, w₂ the proportion (weight) of all 2-sizefamilies of APs among N families, . . . , and w_(i) the proportion(weight) of all i-size families of APs among N families. The variable Lis the largest possible size of a family of APs that exists. Thefollowing holds true:

$\begin{matrix}{{{\sum\limits_{i = 1}^{L}w_{i}} = 1}{and}} & (11) \\{N = {\frac{M}{\sum\limits_{i = 1}^{L}{i\; w_{i}}}.}} & (12)\end{matrix}$

The variable p_(i) is the rate of movement of i-size families (i=1, 2,3, . . . ). In other words,

$\begin{matrix}{p_{i} = \frac{{number\_ of}{\_ moved}{\_ during}{\_ the}{\_ year}{\_ i}\text{-}{size\_ families}}{{total\_ number}{\_ of}{\_ i}\text{-}{size\_ families}}} & (13)\end{matrix}$

The variable a_(ij) is the total collected number of i-size clusters vs.j-size clusters situations among the known-in-advance scan locationdata. For example, a₁₃ represents the total collected number of 1-sizeclusters vs. 3-size clusters, or, as defined above, the total number of1→3 pairs plus the total number of 3→1 pairs. Given this, the totalnumber of 1-size families that have been moved can be found. This numberis determined as follows:

${a_{11} + {k_{12}a_{12}} + {k_{13}a_{13}} + \ldots + {k_{1\; L}a_{1\; L}}} = {a_{11} + {\overset{L}{\sum\limits_{i = 2}}{k_{1\; i}a_{1\; i}}}}$

This value is also equal to w₁Np₁. Thus, the following system ofequations results:

$\begin{matrix}{\mspace{79mu}{{a_{11} + {k_{12}a_{12}} + {k_{13}a_{13}} + \ldots + {k_{1\; L}a_{1\; L}\mspace{11mu}\ldots}} = {w_{1}N\; p_{1}}}} & \left( e_{1} \right) \\{\mspace{79mu}{{a_{22} + {\left( {1 - k_{12}} \right)a_{12}} + {k_{23}a_{23}} + \ldots + {k_{2\; L}a_{2\; L}\mspace{14mu}\ldots}} = {w_{2}N\; p_{2}}}} & \left( e_{2} \right) \\{\mspace{79mu}{{{a_{33} + {\left( {1 - k_{13}} \right)a_{13}} + {\left( {1 - k_{23}} \right)a_{23}} + \ldots + {k_{3\; L}a_{3\; L}\mspace{14mu}\ldots}} = {w_{3}N\; p_{3}}}\mspace{79mu}\vdots\mspace{79mu}\vdots}} & \left( e_{3} \right) \\{{a_{LL} + {\left( {1 - k_{1\; L}} \right)a_{1\; L}} + {\left( {1 - k_{2\; L}} \right)a_{2\; L}} + \ldots + {\left( {1 - k_{{L - 1},L}} \right)a_{{L - 1},L}\mspace{14mu}\ldots}} = {w_{L}N\; p_{L}}} & \left( e_{11} \right)\end{matrix}$

Everything on the left-hand side of the system (e₁)-(e_(L)) is known.Thus, the values for all of the ratios

$\frac{w_{i}p_{i}}{w_{j}p_{j}}$can be found. It is important to note that parameters w_(i) and p_(i) donot depend on whether only the known-in-advance locations scanpopulation is taken into account, or whether the entire population(i.e., known location scans and unknown location observations) are takeninto account.

Consider now the whole population of data from both known-in-advance andunknown locations. The variable b_(ij) is the total collected number ofi-size clusters vs. j-size clusters situations among the entirepopulation of scan and observation data. For the sake of consistency,the notation k_(ij) for the K-values, as used above for only locationsknown-in-advance, is retained in the description below for the entirepopulation of data. However, it is noted that the K-values of the twoscenarios are not necessarily equal because there may be bias ofestimation of K-values to the known-in-advance scan population.

The variable N₁ is the total number of existing different families ofAPs if the entire population (i.e., known location scans and unknownlocation observations) is taken into account. Using logic similar to thedescription immediately above, the following system of equationsresults:

$\begin{matrix}{\mspace{79mu}{{b_{11} + {k_{12}b_{12}} + {k_{13}b_{13}} + \ldots + {k_{1\; L}b_{1\; L}\mspace{11mu}\ldots}} = {w_{1}N_{1}\; p_{1}}}} & \left( f_{1} \right) \\{\mspace{79mu}{{b_{22} + {\left( {1 - k_{12}} \right)b_{12}} + {k_{23}b_{23}} + \ldots + {k_{2\; L}b_{2\; L}\mspace{14mu}\ldots}} = {w_{2}N_{1}\; p_{2}}}} & \left( f_{2} \right) \\{\mspace{79mu}{{{b_{33} + {\left( {1 - k_{13}} \right)b_{13}} + {\left( {1 - k_{23}} \right)b_{23}} + \ldots + {k_{3\; L}b_{3\; L}\mspace{14mu}\ldots}} = {w_{3}N_{1}\; p_{3}}}\mspace{79mu}\vdots\mspace{79mu}\vdots}} & \left( f_{3} \right) \\{{b_{LL} + {\left( {1 - k_{1\; L}} \right)b_{1\; L}} + {\left( {1 - k_{2\; L}} \right)b_{2\; L}} + \ldots + {\left( {1 - k_{{L - 1},L}} \right)b_{{L - 1},L}\mspace{14mu}\ldots}} = {w_{L}N_{1}\; p_{L}}} & \left( f_{L} \right)\end{matrix}$

In the above system of equations (f₁)-(f_(L)), the parameters k_(ij)must be estimated. The values of b_(ij) are known because theinformation is derived from scan data, and all of the ratios

$\frac{w_{i}p_{i}}{w_{j}p_{j}}$are known, as provide above. Therefore, L independent equations existand

$\frac{L\left( {L - 1} \right)}{2}$variables k_(ij) exist. The value of

${\frac{L\left( {L - 1} \right)}{2} - L} = \frac{L\left( {L - 3} \right)}{2}$different k_(ij) parameters, described immediately above, are obtainedduring scan data collection. These parameters are substituted in thesystem of equations (f₁)-(f_(L)), in order to find the remaining Ldifferent k_(ij) parameters.

Thus, the k_(ij) parameters of the entire population of data (i.e.,known and unknown locations) are estimated using a “smart guess” basedon knowledge of some statistics of entire population (e.g., b_(ij)values) and knowledge of some statistics (e.g., K-values) ofknown-in-advance scan location information. In other words, the

$\frac{L\left( {L - 3} \right)}{2}$estimates of the k_(ij) parameters, found as a solution to the system ofequations (e₁)-(e_(L)), are substituted into the system of equations(f₁)-(f_(L)) to find the remaining L k_(ij) parameters.

The techniques and systems disclosed herein may be implemented as acomputer program product for use with a computer system or computerizedelectronic device. Such implementations may include a series of computerinstructions, or logic, fixed either on a tangible medium, such as acomputer readable medium (e.g., a diskette, CD-ROM, ROM, flash memory orother memory or fixed disk) or transmittable to a computer system or adevice, via a modem or other interface device, such as a communicationsadapter connected to a network over a medium.

The medium may be either a tangible medium (e.g., optical or analogcommunications lines) or a medium implemented with wireless techniques(e.g., Wi-Fi, cellular, microwave, infrared or other transmissiontechniques). The series of computer instructions embodies at least partof the functionality described herein with respect to the system. Thoseskilled in the art should appreciate that such computer instructions canbe written in a number of programming languages for use with manycomputer architectures or operating systems.

Furthermore, such instructions may be stored in any tangible memorydevice, such as semiconductor, magnetic, optical or other memorydevices, and may be transmitted using any communications technology,such as optical, infrared, microwave, or other transmissiontechnologies.

It is expected that such a computer program product may be distributedas a removable medium with accompanying printed or electronicdocumentation (e.g., shrink wrapped software), preloaded with a computersystem (e.g., on system ROM or fixed disk), or distributed from a serveror electronic bulletin board over the network (e.g., the Internet orWorld Wide Web). Of course, some embodiments of the invention may beimplemented as a combination of both software (e.g., a computer programproduct) and hardware. Still other embodiments of the invention areimplemented as entirely hardware, or entirely software (e.g., a computerprogram product).

Moreover, the techniques and systems disclosed herein can be used with avariety of mobile devices. For example, mobile telephones, smart phones,personal digital assistants, satellite positioning units (e.g., GPSdevices), and/or mobile computing devices capable of receiving thesignals discussed herein can be used in implementations of theinvention. The location estimate, corresponding expected error of theposition estimate, and/or the probability values can be displayed on themobile device and/or transmitted to other devices and/or computersystems. Further, it will be appreciated that the scope of the presentinvention is not limited to the above-described embodiments, but ratheris defined by the appended claims; and that these claims will encompassmodifications of and improvements to what has been described.

What is claimed is:
 1. A method of estimating a likelihood of a Wi-Fienabled device being located within an estimated geographical area, themethod comprising: identifying at least one Wi-Fi access point in rangeof the Wi-Fi enabled device based on signals received by the Wi-Fienabled device transmitted by the at least one Wi-Fi access point;consulting a reference database to determine for the at least one Wi-Fiaccess point from which signals were received a last-known position ofthe at least one Wi-Fi access point and time information associated withsaid last-known position for describing a most recent time when the atleast one Wi-Fi access point was observed to be at the last-knownposition; estimating a geographical area in which the Wi-Fi enableddevice may be located; and estimating the likelihood of the Wi-Fienabled device being located within the estimated geographical areabased on a probability that the at least one Wi-Fi access point hasrelocated, the probability that the at least one Wi-Fi access point hasrelocated based on at least one of: the most recent time when the atleast one Wi-Fi access point was observed to be at the last-knownposition as indicated by the associated time information, or a number ofthe one or more Wi-Fi access points from which signals were received bythe Wi-Fi enabled device, wherein the likelihood of the Wi-Fi enableddevice being located within the estimated geographical area quantifies aprobability that the estimate of the geographical area is correct. 2.The method of claim 1, wherein probability that the at least one Wi-Fiaccess point has relocated is based on the most recent time when the atleast one Wi-Fi access point was observed to be at the last-knownposition.
 3. The method of claim 2, further comprising determininginformation that characterizes a probability that a Wi-Fi access pointhas moved from its corresponding last-known position.
 4. The method ofclaim 3, wherein the determining the information that characterizes theprobability that the Wi-Fi access point has moved from its correspondinglast-known position comprises: determining a set of Wi-Fi access points,each Wi-Fi access point of the set located at a first geographicposition for the corresponding Wi-Fi access point at a first point intime, and having moved to a second geographic position for thecorresponding Wi-Fi access point at a second point in time; and based onthe set of Wi-Fi access points that moved and based on the amount oftime between the first and second points in time, determininginformation that characterizes the probability that the Wi-Fi accesspoint has moved from its last-known position based on a most recent timewhen the Wi-Fi access point was observed to be at the last-knownposition.
 5. The method of claim 1, further comprising: consulting ahistorical dataset to determine for at least one of the Wi-Fi accesspoints from which signals were received information describing pastrelocations for the at least one Wi-Fi access point; wherein theprobability that the at least one Wi-Fi access point has relocated isfurther based on the information describing past relocations for the atleast one Wi-Fi access point.
 6. The method of claim 5, wherein theinformation describing past relocations for the at least one Wi-Fiaccess point includes an average movement frequency for the at least oneWi-Fi access point.
 7. The method of claim 5, wherein the informationdescribing past relocations for the at least one Wi-Fi access pointincludes an aggregate average movement frequency based on a collectionof movement data for a plurality of Wi-Fi access points.
 8. The methodof claim 1, further comprising displaying on a display deviceinformation based on the estimated likelihood of the Wi-Fi enableddevice being located within the estimated geographical area.
 9. A methodof estimating a likelihood that a Wi-Fi enabled device is located withinan estimated geographical area, the method comprising: identifying atleast one Wi-Fi access point in range of the Wi-Fi enabled device basedon signals received by the Wi-Fi enabled device transmitted by the atleast one Wi-Fi access point; consulting a reference database todetermine one or more clusters of one or more Wi-Fi access points fromthe identified at least one Wi-Fi access point, each cluster having alast-known position; estimating a geographical area in which the Wi-Fienabled device may be located based on a cluster of the one or moreclusters; estimating the likelihood that the Wi-Fi enabled device islocated within the estimated geographical area, the likelihood estimatedbased on a probability that the cluster has relocated, the probabilitythat the cluster has relocated based on at least one of: a time when thecluster was last observed to be at the last-known position, or a clustersize indicating a number of Wi-Fi access points in the cluster, whereinthe likelihood that the Wi-Fi enabled device is located within theestimated geographical area quantifies a probability that the estimateof the geographical area is correct.
 10. The method of claim 9, whereinthe probability that the estimate of the geographical area is correct isa center probability, and the geographical area is an area centered uponan estimated location having the center probability.
 11. The method ofclaim 9, wherein the one or more clusters include a first cluster and asecond cluster that have last-known positions separated by a distancegreater than a transmission range of Wi-Fi access points, such that ifWi-Fi access points of both clusters are identified simultaneously bythe Wi-Fi enabled device, then at least one last-known position must beincorrect.
 12. The method of claim 9, wherein the probability that thecluster has relocated is based on the time when the cluster was lastobserved, and the estimating provides that a newer cluster with newerobservations has a greater likelihood that the Wi-Fi enabled device islocated within the estimated geographical area than an older clusterwith older observations.
 13. The method of claim 9, wherein theprobability that the cluster has relocated is based on the cluster size,and the estimating provides that a larger cluster with more Wi-Fi accesspoints has a greater likelihood that the Wi-Fi enabled device is locatedwithin the estimated geographical area than a smaller cluster with lessWi-Fi access points.
 14. The method of claim 9, wherein the probabilitythat the cluster has relocated is based on a combination of both thetime when the cluster was last observed and the cluster size.
 15. Themethod of claim 9, wherein the probability that the cluster hasrelocated is further based on a number of the one or more clusters. 16.The method of claim 9, wherein the probability that the cluster hasrelocated is further based on a historical dataset that includesinformation describing past relocations of at least one Wi-Fi accesspoint in the cluster.
 17. The method of claim 16, wherein theinformation describing past relocations includes an average movementfrequency.
 18. The method of claim 9, wherein the probability that thecluster has relocated is further based on a number of Wi-Fi accessespoints surrounding at least one Wi-Fi access point in the cluster.
 19. Asystem comprising: a Wi-Fi enabled device configured to identify aplurality of Wi-Fi access points in range of the Wi-Fi enabled device;and a non-transitory computer readable medium storing programinstructions that when executed on the Wi-Fi enabled device or on aserver, are operable to: consult a reference database to determine oneor more clusters of one or more Wi-Fi access points from the identifiedplurality of Wi-Fi access points, each cluster having a last-knownposition, and estimate a likelihood that the Wi-Fi enabled device islocated within an estimated geographical area based on a probabilitythat a cluster of the one or more clusters has relocated, theprobability estimated based on at least one of: a time when the clusterwas last observed to be at the last-known position, or a cluster sizeindicating a number of Wi-Fi access points in the cluster, wherein thelikelihood that the Wi-Fi enabled device is located within the estimatedgeographical area quantifies a probability that the estimate of thegeographical area is correct.
 20. The system of claim 19, wherein theprobability that the estimate of the geographical area is correct is acenter probability, and the geographical area is an area centered uponan estimated location having the center probability.